Cambridge Philosophical Society. 3J7 



for the present problem, except by estimating the density of saturated 

 vapour at any temperature (the corresponding pressure being known 

 by Regnault's researches already published) according to the approxi- 

 mate laws of compressibility and expansion (the laws of Mariotte 

 and Gay-Lussac, or Boyle and Dalton). "Within the limits of natural 

 temperature in ordinary climates, the density of saturated vapour is 

 actually found by Regnault {Etudes Hygrome'triques in the Annates 

 de Chimie) to verify very closely these laws ; and we have reason to 

 believe from experiments which have been made by Gay-Lussac and 

 others, that as high as the temperature 100° there can be no consi- 

 derable deviation ; but our estimate of the density of saturated va- 

 pour, founded on these laws, may be very erroneous at such high 

 temperatures as 230°. Hence a completely satisfactory calculation 

 of the proposed scale cannot be made till after the additional experi- 

 mental data shall have been obtained ; but with the data which we 

 actually possess, we may make an approximate comparison of the 

 new scale with that of the air-thermometer, which at least between 

 0° and ] 00° will be tolerably satisfactory. 



The labour of performing the necessary calculations for effecting 

 a comparison of the proposed scale with that of the air-thermometer, 

 between the limits 0° and 230° of the latter, has been kindly under- 

 taken by Mr. William Steele, lately of Glasgow College, now of 

 St. Peter's College, Cambridge. His results in tabulated forms were 

 laid before the Society, with a diagram, in which the comparison 

 between the two scales is represented graphically. 



In the first table, the amounts of mechanical effect due to the 

 descent of a unit of heat through the successive degrees of the air- 

 thermometer are exhibited. The unit of heat adopted is the quan- 

 tity necessary to elevate the temperature of a kilogramme of water 

 from 0° to 1° of the air-thermometer; and the unit of mechanical effect 

 is a metre-kilogramme ; that is, a kilogramme raised a metre high. 



In the second table, the temperatures according to the proposed 

 scale, which correspond to the different degrees of the air- thermo- 

 meter from 0° to 230°, are exhibited. [The arbitrary points which 

 coincide on the two scales are 0° and 100°.] 



Note. — If we add together the first hundred numbers given in the 

 first table, we find 135 - 7 for the amount of work due to a unit of 

 heat descending from a body A at 100° to B at 0°. Now 79 such 

 units of heat would, according to Dr. Black (his result being very 

 slightly corrected by Regnault), melt a kilogramme of ice. Hence 

 if the heat necessary to melt a pound of ice be now taken as unity, 

 and if a metre-pound be taken as the unit of mechanical effect, the 

 amount of work to be obtained by the descent of a unit of heat from 

 100° to 0° is 79 x 135-7, or 10,700 nearly. This is the same as 

 35,100 foot-pounds, which is a little more than the work of a 

 one-horse-power engine (33,000 foot-pounds) in a minute ; and 

 consequently, if we had a steam-engine working with perfect ceco- 

 nomy at one-horse-power, the boiler being at the temperature 100°, 

 and the condenser kept at 0° by a constant supply of ice, rather 

 less than a pound of ice would be melted in a minute. 



